Simplify the following expression: $t = \dfrac{6p^3 - 14p^2}{-10p^3 + 10p^2}$ You can assume $p \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $6p^3 - 14p^2 = (2\cdot3 \cdot p \cdot p \cdot p) - (2\cdot7 \cdot p \cdot p)$ The denominator can be factored: $-10p^3 + 10p^2 = - (2\cdot5 \cdot p \cdot p \cdot p) + (2\cdot5 \cdot p \cdot p)$ The greatest common factor of all the terms is $2p^2$ Factoring out $2p^2$ gives us: $t = \dfrac{(2p^2)(3p - 7)}{(2p^2)(-5p + 5)}$ Dividing both the numerator and denominator by $2p^2$ gives: $t = \dfrac{3p - 7}{-5p + 5}$